Figure REF  shows examples of our visualization tools of test functions \(f^{s\mid vt}\) . Figure REF  (a) illustrates our modified functional boxplot for \(f^{s\mid vt}\)  obtained from simulated data with a S\(\mid \) VT covariance. The obtained test functions are first ordered by the modified band depth [1]}, then the 50% central region that consists of the 50% test functions with largest band depth values is shown as the area bordered by the blue box. The original functional boxplot of [2]} fills the central region with solid magenta color. To better show the relative position of test functions to zero, we fill the central region above zero with solid magenta, but fill the central region below zero with dashed magenta lines. These two parts in the central region suggest that the underlying covariance is S\(\mid \) VT. The upper- and lower-blue curves are the whiskers, which are the envelop of test functions within the inflated central region by 1.5 times the height of the central region at each \(u\) . Figure REF  (b) and (c) are discussed in Section REF  after the testing procedure is introduced.
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